Properties

Label 1014.3.f
Level $1014$
Weight $3$
Character orbit 1014.f
Rep. character $\chi_{1014}(577,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $100$
Newform subspaces $12$
Sturm bound $546$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1014.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 12 \)
Sturm bound: \(546\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1014, [\chi])\).

Total New Old
Modular forms 784 100 684
Cusp forms 672 100 572
Eisenstein series 112 0 112

Trace form

\( 100 q + 4 q^{2} - 12 q^{5} - 8 q^{8} + 300 q^{9} - 24 q^{11} + 32 q^{14} + 24 q^{15} - 400 q^{16} + 12 q^{18} + 24 q^{20} - 24 q^{21} + 96 q^{22} + 112 q^{29} + 48 q^{31} - 16 q^{32} - 72 q^{33} - 72 q^{34}+ \cdots - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(1014, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1014.3.f.a 1014.f 13.d $4$ $27.629$ \(\Q(\zeta_{12})\) None 78.3.f.a \(-4\) \(0\) \(-12\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta_1-1)q^{2}+\beta_{3} q^{3}-2\beta_1 q^{4}+\cdots\)
1014.3.f.b 1014.f 13.d $4$ $27.629$ \(\Q(\zeta_{12})\) None 78.3.l.b \(-4\) \(0\) \(6\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta_{2}-1)q^{2}+(-\beta_{3}+\beta_{2}-\beta_1)q^{3}+\cdots\)
1014.3.f.c 1014.f 13.d $4$ $27.629$ \(\Q(\zeta_{12})\) None 1014.3.f.c \(-4\) \(0\) \(8\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta_1-1)q^{2}-\beta_{3} q^{3}+2\beta_1 q^{4}+\cdots\)
1014.3.f.d 1014.f 13.d $4$ $27.629$ \(\Q(\zeta_{12})\) None 78.3.l.a \(-4\) \(0\) \(12\) \(10\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta_{2}-1)q^{2}+(\beta_{3}-\beta_{2}+\beta_1)q^{3}+\cdots\)
1014.3.f.e 1014.f 13.d $4$ $27.629$ \(\Q(\zeta_{12})\) None 78.3.l.a \(4\) \(0\) \(-12\) \(-10\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta_{2}+1)q^{2}+(\beta_{3}-\beta_{2}+\beta_1)q^{3}+\cdots\)
1014.3.f.f 1014.f 13.d $4$ $27.629$ \(\Q(\zeta_{12})\) None 1014.3.f.c \(4\) \(0\) \(-8\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta_1+1)q^{2}-\beta_{3} q^{3}-2\beta_1 q^{4}+\cdots\)
1014.3.f.g 1014.f 13.d $4$ $27.629$ \(\Q(\zeta_{12})\) None 78.3.l.b \(4\) \(0\) \(-6\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta_{2}+1)q^{2}+(-\beta_{3}+\beta_{2}-\beta_1)q^{3}+\cdots\)
1014.3.f.h 1014.f 13.d $8$ $27.629$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 78.3.l.c \(-8\) \(0\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{2})q^{2}+(-\beta _{3}+\beta _{6})q^{3}+2\beta _{2}q^{4}+\cdots\)
1014.3.f.i 1014.f 13.d $8$ $27.629$ 8.0.\(\cdots\).1 None 78.3.f.b \(8\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\beta _{6})q^{2}+\beta _{1}q^{3}-2\beta _{6}q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
1014.3.f.j 1014.f 13.d $8$ $27.629$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 78.3.l.c \(8\) \(0\) \(6\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{2})q^{2}+(-\beta _{3}+\beta _{6})q^{3}+2\beta _{2}q^{4}+\cdots\)
1014.3.f.k 1014.f 13.d $24$ $27.629$ None 1014.3.f.k \(-24\) \(0\) \(-8\) \(-24\) $\mathrm{SU}(2)[C_{4}]$
1014.3.f.l 1014.f 13.d $24$ $27.629$ None 1014.3.f.k \(24\) \(0\) \(8\) \(24\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1014, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1014, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)